Dustin's Reflection

Well...we finished the book this week(yes!!!). It was very slow at first, but it got better. It was interesting and I'm kinda interested in seeing the movie. The questions weren't very hard and they were easy points, which i needed. Most questions were easy to find, being that the chapters had titles. From what I understand, we have a giant trig test coming up. I don't remember alot of the stuff and I'm kinda nervous b/c I really need to pass this test. I need help with how to use all of the half angle fomulas and all of the properties of the functions. I'm just gonna need some help remembering how to do stuff and some refreshers of the formulas. Any help is much appreciated. I really don't know what else to say and I know I'm supposed to explain something. Sooooo, I guess thats it.

Chapter 13 Sequences and Recursive Definitions

Sequences

A sequence is simply a list of numbers.

There are two main types of sequences:
Arithmetic - where you add or subtract
Geometric - where you multiply
(*Note: division is considered Geometric. For example: If a sequence divides by three, it is considered to be multiplied by one-third.

Formulas to find a term:

Arithmetic

tn-t'+(n-1)d

n=term #

t'=first term

d=what you add

tn=term#_in sequence

Geometric

tn=t'∙r^(n-1)

r= what you multiply by

Recursive Definitions

A recursive Definition is a formula for a sequence that involves a previous term. [a(n-1)]

an= (an-1/3)

Amy's Reflection #28

here are some stuff from chapter 6 + examples...

Ellipses

Steps:
1. find the center
2. determine the major axis
3. find the vertex (± √big denom)
4. find the other intercept ( ± √small denom)
5. find the focus (c^2 = a^2 + b^2)
6. determine the length of the major axis (2√big denom)
7. find the length of the minor axis (2√small denom)
8. finally graph

Example 1: Graph the following ellipse. Find its major intercepts, length of the major axis, minor intercepts, length of the minor axis, and foci.

x^2/4 + y^2/9 = 1

This ellipse is centered at (0, 0). Since the larger denominator is with the y variable, the major axis lies along the y-axis.

Since a^2 = 9 then a = 3 & Since b^2 = 4

then b = 2Major intercepts: (0, 3), (0, –3)

Length of major axis: 2 √9 = 6

Minor intercepts: (2, 0), (–2, 0)

Length of minor axis: 2√4 = 4
c^2 = a^2 + b^2
= 9 - 4
= 5
= √5

Foci: (0, √5) , (0, -√5)

then you graph your points..

Parabolas:

how to find the axis of symmetry, vertex, focus, & directrx??

1.) to find the axis of symmetry: x = -b/2a

2.) for the vertex: (-b/2a, f(-b/2a)) or use complete the square:
y = (x+a)^2 + b.....a & b are numbers and (-a,b) = vertex

3.) to find the focus: 1/4p= the coefficient of x^2 and then add p

Note:
*If opens up, add to y value from vertex, if opens down, subtract
*If opens right, add to x value to vertex, if opens left, subtract)

4.) directrix: is p units behind the vertex

Note:
*If opens up, subtract; if opens down, add from y-value of vertex.*If opens right, subtract x-value*If opens left, add x-value

Example: x^2 + 1

~vertex:
x = -b/2a
x = 0/2(1) = 0
0^2 + 1 = 1
(0,1)

~Focus:
1/4p = 1
4p = 1
p = 1/4
(0, 1 + 1/4)
(0, 5/4)

~directrix:
y = 1 - 1/4
y = 3/4

can someone please explain recursive definition? now someone has a question to answer..

Taylor "blog comments" for 24 Feb

Sice not a single other person other than myself has posted anything math related much less a question to answer i am going to post another review blog to count for my blog comments of this week

because soon we will be retesting on trig ill start with the early parts of trig for this blog

Angles are measured in DEGREES (possibly with either minutes' or minutes' andseconds")
and RADIANS


To find minutes
multiply what is behind the decimal by 60
and take whole number as minutes'

To find seconds
multiply what is behind the decimal of minutes by 60
then whats behind that decimal by 3600 to get seconds'

To get radians

degrees x pi/180degrees

((***Remember to always ues exact answers))
((*** Remember to never plug pi into calculator))

Flatland Chapters 5-8

1. They are all lines in a 2D perspective. This was the point of looking at a penny. You aren't above the shape to be able to see it. You are even with a side so you can only see one side at a time.

2. hearing, feeling and color.

3. The shapes painted themselves to be able to distinguish themselves. This is related to the class they are in. Therefore, it is similar to our fashion choices. The brand of clothing does this in our society. In addition, we use color and style to stand out from everyone else or to blend in.

4. This is an opinion. As long as you support it correctly it is right. However, the narrator is a middle-class square. Some people did not realize this. In addition, it has to be supported with facts from the book! Saying he is a nice guy or that he seemed to know what was going on is not adequate.

5. This is an opinion. However, satirize means to poke fun at something while still trying to make a point. Utopian means perfect. Is this society really perfect with the limitations placed on women and lower classes?

Writing Activity: Make sure this is at least a paragraph... Mrs. Mustian would be appalled that some paragraphs are two sentences.. However, if everyone is a line, how can you animate that?

Chapter 13 Sequences and Recursive Definitions

Sequences

A sequence is simply a list of numbers.

There are two main types of sequences:
Arithmetic - where you add or subtract
Geometric - where you multiply
(*Note: division is considered Geometric. For example: If a sequence divides by three, it is considered to be multiplied by one-third.

Formulas to find a term:

Arithmetic

tn-t'+(n-1)d

n=term #

t'=first term

d=what you add

tn=term#_in sequence

Geometric

tn=t'∙r^(n-1)

r= what you multiply by

Recursive Definitions

A recursive Definition is a formula for a sequence that involves a previous term. [a(n-1)]

an= (an-1/3)

Taylor reflection for 21 feburary

Brob said that while she is out since she is not able to teach anything new we can post information and questions from old chapters
someting i really understand from the past are
The steps for condensing logs
First you have to remember the relations
Mn = m+n
m/n = m-n
m^k = k log M
sub b B^k = k
b^log sub b^k = K

so any problem will fit into one of these relations
Ex: expand log sub b MN^2
Log sub b M + 2 Log sub b N


STILL....
What I do not understand is how to work is the solving for exponent part that includes
Sandwiching and flipping the fraction
For example
X^5 + X^-2 / X ^-3
So now I don’t understand how in my notes the next step is
X^2/X^2 times X^5 + 1/X \^3 times 1/1 all over 1/X^3
I really think I need the rules for flipping fractions and when to sandwich explained simply to me

Alicia's Reflection #26

Some more on Flatland.....

Chapter 3

The size of a full grown inhabitant of Flatland may be estimates at about eleven inches. The women in Flatland are straight lines. The soldiers and lower classes of workmen are triangles with two equal sides. The middle class consists of equilateral or equal-sided triangles. The professional men and gentlemen are squares. The narrator of the book belongs to this class. The nobility are hexagons. It is a law of nature that a male child has one more side than his father.

Chapter 4

Women are compared to needles. There are 3 rules the women must follow. 1) Every house shall have one entrance in the Eastern side, for the use of Females only and must enter in a respectful manner. 2) No female shall walk in any public place without continually keeping up her peace-cry, under penalty of death. 3) Any female, duly certified to be suffering from St. Vitus's Dance, fits, chronic cold accompanied by violent sneezing, or any disease necessitating involuntary motions, shall be instantly destroyed. Females must always move their backs from right to left in any public place to show their presence.

Alicia's Reflection #25

Okay so I am doing my blogs kind of late because I've been in Disney World for danceteam Nationals and I did not bring my laptop on the trip. So I am going to review some things from Flatland since thats what we are reading right now in class.

Chapter 1

All of the people in the novel live in Flatland and the readers live in Spaceland. Everyone in Flatland are shapes. Depending on gender, class, jobs, etc determines their shape. Some shapes include straight lines, triangles, squares, pentagons, hexagons, and other figures.

Chapter 2

There is no sun in Flatland nor heavenly bodies which is the reason for it being impossible to determine the North. There are no windows in their houses. The most common house is five-sided or pentagonal figure. On the east side of the houses are the womens doors and on the west side of the houses are the mens doors which are much bigger doors than the womens. The south side or floor is usually doorless. Square and triangular houses are not allowed.

devin's reflection

To solve anything bigger than a quadratic

1. Factor by graphing
-must have even number of terms

2. Quadratic form
-must have only 3 terms
-1st term must=2nd exponent x2 last term must be a #
-1-make g=x^exponent/2 so you get g^2+g+#
-2-do quadratic formula factor complete the square
-3-plug in for g

3. rational root theorem
-1-find all possible roots
-p/q where p is all factors of the constant q is the factors of leading coeff.
-2-check to see which roots work in table
-3-do synthetic division to factor all roots that work
-4-solve the quadratic

Ex. x^3+5x^2-4x-20=0
(x^3+5x^2)-(4x+20)=0
x^2(x+5)-4(x+5)=0
(x^2-4)(x+5)=0
X^2-4=0
x^2=4
x=+-2

x+5=0
x=-5

=(2,0)(-2,0)(-5,0)

Stephen's reflection

ok so we start school again tomorrow :/..ohh well im not looking forward to it but at least all we gotta do is read a bit. so i mainly remember the sequences which are arithmetic and geometric.

Arithmetic - where you add or subtract
Geometric - where you multiply
(*Note: division is considered Geometric. For example: If a sequence divides by three, it is considered to be multiplied by one-third.

ok so thats all i really rmember and i need help on solving some of these problems

Stephen's late post

ok so this week was long and i forgot everything bout school soo this is late. these are formulas for arithmetic and geometric.

Arithmetic:
tn-t'+(n-1)d
n=term #
t'=first term
d=what you add
tn=term#_in sequence


Geometric
tn=t'∙r^(n-1)
r= what you multiply by

Again i dont really know much so idk whatr i needa know so i guess i just needa be refreshed a bit on a few stuff.

Question, since no one post them anymore

Does anyone post questions anymore????????

Terrio's Reflection

So I was flipping through my binder and I came across a bunch of old formulas that I almost forgot about. Here they are:

Area of a non-right triangle
A=1/2(leg)(leg)sin(angle between)

Area of Right Triangles
A=1/2bh

SOHCAHTOA
sinΘ=opposite leg/hypotenuse
cosΘ=adjacent leg/hypotenuse
tanΘ=opposite leg/adjacent leg

Law of Sines
sinA/a - sinB/b = sinC/c
(used when you know pairs or opposites in a non-right triangle)

Law of Cosines
(opposite leg)²=(adjacent leg)² + (other leg)² - 2(adjacent leg)(adjacent leg)cos°

Area of Inscribed Shapes
A=nr²sinΘcosΘ

Now I know how to use most of these, but the area of Inscribed Shapes is kind of fuzzy to me. I don't even remember learning about that

Reflection

Since we didnt have school last week, I'll just go over random things from Ch. 13.

Sigma Notation

- To evaluate-plug in the numbers between your limits of summation into the summand.
Adding each term to form a series.

- Examples:
Give each series in expanded form

1) 6
sigma 4K = 8,12,16,20,24
K=2

2) 5
sigma 3k+1=4,7,10,13,16
n=1

Yea so thats how you expand Sigma Notation. One thing I had problems with on the test was the constant of variation. If anyone can help me with that, it would be cool.

Stephanie's Reflection

Limacon
r = a+b sin theta
r = a+b cos theta

Cardioid
a-b sin theta
a-b cos theta

Rose
r = a sin n theta
r = a cos n theta
n is how many petals

Archimedes Spiral
r = a theta +b

Logarithmic Spiral
r=a^theta b

Converting
polar to rectangular
x=r cos theta
y=r sin theta

rectangular to polar
r=+/- sqrt x^2 + y^2
theta is (x/y)

Trig Chart:

0°
sin0=0
cos0=1
tan0=undefined
sec0=1
cot0=0

30°
sinπ/6=1/2
cosπ/6=√3/2
tanπ/6=√3/3
cscπ/6=2
secπ/6=2 √3/3
cotπ/6=√3

45°
sinπ/4=√2/2
cosπ/4=√2/2
tanπ/4=1
cscπ/4=√2
secπ/4=√2
cotπ/4=1

60°
sinπ/3=√3/2
cosπ/3=1/2
tanπ/3=√3
cscπ/3=2 √3/3
secπ/3=2
cotπ/3=√3/2

90°
sinπ/2=1
cosπ/2=0
tanπ/2=undefined
cscπ/2=1
secπ/2=undefined
cotπ/2=0

Chapter 13 Sequences and Recursive Definitions

Sequences

A sequence is simply a list of numbers.

There are two main types of sequences:
Arithmetic - where you add or subtract
Geometric - where you multiply
(*Note: division is considered Geometric. For example: If a sequence divides by three, it is considered to be multiplied by one-third.

Formulas to find a term:

Arithmetic

tn-t'+(n-1)d

n=term #

t'=first term

d=what you add

tn=term#_in sequence

Geometric

tn=t'∙r^(n-1)

r= what you multiply by

Recursive Definitions

A recursive Definition is a formula for a sequence that involves a previous term. [a(n-1)]

an= (an-1/3)

Amy's Reflection #27

i hope everyone is enjoying their time off..well anyway, im just gonna post a review of something so we don't forget what we learned in the past...

1.) area of a non right triangle = 1/2 (leg)(leg)SIN(angle b/w)

Example: non-right triangle: HIJ (left to right)H = 65 degrees, j = 2, i = 6. Find the area.

A = (1/2)(2)(6)sin(65)

A = 5.438

2.) Law of Sines(used to non-right triangles):

Sin A/a = Sin B/b= Sin C/c

Example: you have a triangle with the sides 4 and 5 & you also have an angle of 30 degrees.

A = 1/2 (4) (5) Sin 30 degrees

A = 10 Sin 30 degrees which is aproximately = 5

3.) Law of Cosines (used when you can't use Law of Sines):

(opposite leg)^2 = (adjacent leg)^2 + (other adjacent leg)^2 - 2(adjacent leg) (adjacent leg) cos (angle between)

Example: you have a triangle with the sides of 5, 6, and 7. find the angle between 5 and 6.

7^2=6^2+5^2-2(5)(6)

cos a7^2-6^2-5^2= 2(5)(6)

cos acos a= 7^2-6^2-5^2 / -2(6)(5)

a= cos-1 ((7^2-^6^2-5^2)/(-2(5)(6))

a= 78.463 degrees

4.) For any line : m = tan (alpha)
**m = slope , (alpha) = angle of inclination

5.) For a conic: tan 2 (alpha) = B/A-C
**if A=C then pie/4 (always)
**A = coefficient of x^2, B = coefficient of xy, C = coefficient of y^2

Examples:

1. Find the angle of inclination of x^2 - 2xy + 3y^2 = 1.

tan 2 (alpha) = B/A-C

A = 1 , B = -2 , C = 3

tan 2 (alpha) = -2/1 -3 = 1

tan 2 (alpha) = 1

2A = tan^-1 (1)

2 (alpha) = 45 , 225

alpha = 45/2 , 225/2

alpha = 22.5 , 112.5

2. x^2 + y^2 - 3xy + 4x - sqrt.

x = 1alpha = 1 (because A = 1 & C = 1 so A = C)

hope that refreshened your minds...

Taylor reflection for 14 February 2010

I apologize for my reflection being so late i was in vegas and there was barely any cell phone service much less internet service

so ill post my study sheet for the test

Arithmetic= tn= t1 + (n-1) d
Geometric= tn= t1 * r ^ n-1

tn= actual number
n= address of a number in a series

Sn Arithmetic= Sn= n (t1 + tn) /2
Sn Geometric= Sn= t1 (1 - r)^n /1-r

LIMIT -> 1- infinity
polynomial equations uses rules always
rules: t= top b=bottom
t=b: coefficients so the coefficient of the top hightest exponent over the coefficient of the bottom highest exponent
t>b: infinity
t
all other limit problems plug in 100, 1000, 10000 for n in the calculator and record results for each then determine what number the results are headed toward

sum of series only used when r<1>1 then no solution b/c it diverges)
T2 over T1 to get r


Sigma has three parts

a top number
a middle number
a bottom number

top is called limit of summation
middle is called the summand
bottom is called index

top is the address of the last number in given series
middle is the result of the tn formula
bottom is what number you start counting at

if the equation is arithmetic then the bottom number will be 1
if the equation is geometric then the bottom number will be 0


when asked to evaluate for a sigma problem you plug in the numbers including and inbetween the bottom and the top numbers
so if the bottom number is one and the top number is 5 then you would plug in 1, 2, 3, 4, 5 for the variable of the middle equation
and add the results of each plug in together to get final answer


when asked to express then you draw the sigma sign and fill in the top middle and bottom parts



i think i really understand this chapter
ill post again with questions from another chapter later
hope this helps
if anyone needs any explaning or further help dont be afraid to ask!

Amy's Reflection #26

ok i'm just gonna do a whole bunch of examples from chapter 13 to help jog y'all's memory, kk??

Examples:

1. Find the 32nd term in the sequence: 1,4,7,10...
*figure out whether this sequence is arithmetic or geometric.
*arithmetic:because you're adding 3 each time.
*use the arithmetic formula: tn=t1+(n-1)d
*you are looking for "n" in the formula. So you plug in 32 wherever "n" is in the formula.
*So you get t32=1+(32-1)(3)
*that simplifies to =1+(31)(3)
*So t32=94

2. lim (n infinity) sin (1/n)
sin(1/100) = .010
sin(1/1000) = .0010
sin(1/10000) = .00010

lim (n infinity) n+5/n = 1, because the degree is the same, so the coefficients equal 1

3. where the values of x converge
1+(x-2)+(x-2)^2+(x-2)^3+
r=x-2
x-2<1
-1<1
1<3

4.In the arithmetic sequence:3,5,7,9-- find the 28th term.
t28=3+(27)(2)
t28=3+54
t28=57

5. In the geometric sequence: 2,4,8,16-- find the 10th term
t10= 2*2^9
t10= 2*512
t10= 1024

6. Find the sum of the first ten terms of the series:
2 - 6 + 18 - 54 +...
s10 = 2(1 - (-3)^10) / 1 - (-3)
s10 = -29, 524

*(2 being the first number in the problem, -3 being what you multiply each number by
to get the next term)

7. Find the sum of the first 25 terms of the arithmetic series:
11 + 14 + 17 + 20 +...
tn = 11 +(25 - 1)3
tn = 83
s25 = 25(11 +83) / 2
s25 = 1175

*(11 being the first number in the sequence, 3 being the number you add, Plug 25 into the
n-1 formula because your looking for the 25th term)

And for those who have trouble with the problems the involve sigma:

alrighty so say you have this problem...

write the series expanded form.

the limits of summation are 4 and k=1. the index is k. and the summand is 5k.

to expand it, your answer would be 5+10+15+20.

*you have to have 4 numbers in the series becaue thats the number that is the limit of summation. your summand is 5k so you would multiply 1*5, 2*5, 3*5, 4*5 and your answer is 5+10+15+20.

hoped that help...

Stephanie's Reflection

tn-t1+(n-1)d (arithmetic)
sn=(n(t1+tn))/2

• n is term number
• t1 is first term
• d is what you add
• tn is term number in the sequence

tn=t'∙r^(n-1) (geometric)
sn=(t1(1-r^n))/1-r

• r is what you multiply by

lim/n infinity

• if the degree of the top is equal to the degree of the bottom then the answer is the coefficient
• if the degree of the top is greater than the degree of the bottom the answer is infinity
• if the degree of the top is less than the degree of the bottom the answer is 0
• if the rules don't apply, use your calculator

for geometric sequences if the absolute value of r is less than 1 then it goes to 0

the sum of infinite series can only be found when a geometric sequence where the absolute value of r is less than 1

s=t1/1-r

• if the absolute value of r is not less than 1, the series diverges (doesn't approach a number)
• if the absolute value of r is less than 1, the series approaches a number

Stephen's Reflection

Ok so we still on ch 13. This chapter is kinda sorta easy for right now because we basically use the same formulas which are arithmetic and geometric. Im going to explain the formulas for series.

Arithmetic series: Sn=(n(t1+tn))/2

Geometric series: Sn=(t1(1-r^n))/1-r

Ex: Find the sum of the first 25 terms of the series...11+14+17+20+...

first you find tn which is t25 and use the arithmetic formula which is t1+(n-1)d so it will be 11+(24)(3)=83.

Then you plug in the arithmetic series formula: Sn=25(11+83)/2=1175 and that is your answer.

The only thing i have problems with is what do i do with n when they dont tell me how many terms there are?

Stephen

Dustin's Reflection

Didn't learn too much new stuff this week. I'm ready to start reading flatland being that it will help my grade. I missed the whole lesson on limits and didn't know what to do for them on the quiz. I could really use some help on them if possible. I'm just gonna help with some identification because B-rob said that alot of ppl missed those problems on the test.

Say the sequence is: 1,3,6,10,15,21,...

You can see that you are adding 2, then 3,...

Just because you are adding does not make it arithmetic though. In order for it to be arithmetic, the sequence must add or subtract the same number each time. Being that this sequence adds a different number each time, this sequence is not classified as arithmetic or geometric.

Same rules apply for geometric. If it does not multiply by the same number each time, it is not geometric. NEITHER IS ALWAYS A CHOICE.

Taylor ((birthday)) reflection

so my blog is a bit late but lets see yesterday was my birthday and the saints actually won the super bowl
wow.

since everyone feared the limit lesson of chapter i guess thats what ill reflect on

there are two types of limit equations
the ones that use rules and the ones that use a calculator

the ones that use rules have simple hints to memorize for solving
the only ones that use rules are the polynomial equations problems

memorize this

((the rules))
t- top lead co
b- bottom lead co

t=b then coefficients
t>b then infinity
t
if you get a problem with a limit that is a polynomial equation
use the rules.
each and every time

the other type of problem is the one that calls for the use of a calculator
every single problem with limits that is not a polynommial equation calls for the use of a calculator

all you have to do is plug in for n three different times with
100
1000
10000
then plug into calculator
record what each outcome is and decipher what the numbers are headed toward which will then be your answer





what i dont understand is the sigma notation lesson
can anyone give me simplified hints or steps for working the sigma exuations

Alicia's Reflection # 25

Alrighty so GOOO SAINTSS.... Im not really a big fan but im happy for them for making history!!! Okay well last week we learned Infinite sequences and series and Sums of Infinite Series.

13-4 Infinite Sequences and Series

*lim
n-infinity: if the degree of the top= the degree of the bottom, then the answer is the coefficients.

Example:

lim n^2+1/2n^2-3n = 1/2
n-infinity

*lim
n-infinity: if the degree of the top is > the degree of the bottom, then your answer is infinity

Example:

lim 7n^3/4n^2-5 = infinity
n-infinity

*lim
n-infinity: if the degree of the top is < the degree of the bottom, then your answer is 0

Example:

lim 5n^2/3n^3+7 = 0
n-infinity

***If no rules apply, then you have to use your calculator to find what the sequence is approaching.

13-5 Sums of Infinite Series

*they can only be found with a geometric serires where /r/<1

Formula: S= t1/1-r

Example: 9-6+4

r= -6/9= -2/3 geometric

/-2/3/<1

S= 9/(1-(-2/3))= 27/5

Example: Write .45 repeating as a fraction

45/100-1= 45/99= 5/11


What i could use some help with is recursive definitions and sigma notation!! Thanks :)

Chapter 13 Sequences and Recursive Definitions

Sequences

A sequence is simply a list of numbers.

There are two main types of sequences:
Arithmetic - where you add or subtract
Geometric - where you multiply
(*Note: division is considered Geometric. For example: If a sequence divides by three, it is considered to be multiplied by one-third.

Formulas to find a term:

Arithmetic

tn-t'+(n-1)d

n=term #

t'=first term

d=what you add

tn=term#_in sequence

Geometric

tn=t'∙r^(n-1)

r= what you multiply by

Recursive Definitions

A recursive Definition is a formula for a sequence that involves a previous term. [a(n-1)]

an= (an-1/3)

Reflection #25

YEAH CUHHH! The Saints just won that CUH!

So um I like the Colts, that's my favorite team and I'm pumped for the Saints for finally winning, I don't know why but I don't even care that the Colts lost. But here's something I remember learning. Sequences and Series:

formulas:

1. Arithmetic- tn=t1+(n-1)d

n=term # t1=first term d=what you add

2. Geometric- tn=t1*r^(n-1)

r= what you multiply by n=term # t1=first term d=what you add


Ex.
6, 12, 24,.....

This is a Geometric sequence so you'd use the formula tn=t1*r^(n-1)

You would have 6*2^(n-1)

If you wanted to know the 4th term you would plug the 4 into the n and this is what you would get.

6*2^(4-1)
6*2^(3)
6*8
48

Now one thing I don't remember as of right now isssss, everything we did last week, I don't really remember anything from last week right now.

Stephanie's Reflection

tn-t1+(n-1)d (arithmetic)
sn=(n(t1+tn))/2

• n is term number
• t1 is first term
• d is what you add
• tn is term number in the sequence

tn=t'∙r^(n-1) (geometric)
sn=(t1(1-r^n))/1-r

• r is what you multiply by

lim/n infinity

• if the degree of the top is equal to the degree of the bottom then the answer is the coefficient
• if the degree of the top is greater than the degree of the bottom the answer is infinity
• if the degree of the top is less than the degree of the bottom the answer is 0
• if the rules don't apply, use your calculator

for geometric sequences if the absolute value of r is less than 1 then it goes to 0

the sum of infinite series can only be found when a geometric sequence where the absolute value of r is less than 1

s=t1/1-r

• if the absolute value of r is not less than 1, the series diverges (doesn't approach a number)
• if the absolute value of r is less than 1, the series approaches a number

Amy's Reflection #25

13 -4 Infinite Sequences & Series

Rules:

lim
n (infinity)

(used to plug in large numbers)

1. if the degree of the top = the degree of the bottom then the answer is the coefficients

2. if the degree of the top is > the degree of the bottom = infinity

3. if the degree of the top is < the degree of the bottom is 0

* if the rules don't apply you will have to use your calculator to find what the sequence is approaching

* for geometric sequences if |r| < 1 then it goes to 0

Examples:

1. Rule #1

3n^3 + 5n^2 + 6n^4/2n^3 + 5n^4 = 6/5

2. Rule #2

lim cos (1/n)
n (infinity)

cos(1/100) = .99995
cos(1/1000) = 1
cos(1/10000) = 1

= 1

3. Rule #3

5n^2 + √n/3n^3 + 7 = 0

4. no rule

lim (-10)^n
n (infinity)

(-10)^100 = -10000
(-10)^1000 = -100000

= -(infinity)

13 - 5 Sum of Infinite Series

*can only be found when a geometric sequence where |r|<1

Formula: S = t1/1-r

*if |r| is not less than 1 we say the series diveges - doesn't approach a #

* if |r|<1 then we say the series approaches a #

Examples:

1. Find the sum of the infinite series: 9 - 6 + 4

(geometric)

r = -6/9 = -2

|-2/3| < 1

S = 9/(1 - (-2/3)) = 27/5

2. For what values of x does the series converges? : 1 + (x-2) + (x+2)^2 + (x-2)^3

|x-2/1| < 1

-1 < x < 1

1 < x < 3

ok i need help with the problems that involves sigma, so if anyone can help me with that that would be great...

Stephen's Reflection

Ok so this week we are on chapter 13. This chapter is kinda sorta easy for right now because we basically use the same formulas which are arithmetic and geometric. Im going to explain the formulas for series.

Arithmetic series: Sn=(n(t1+tn))/2

Geometric series: Sn=(t1(1-r^n))/1-r

Ex: Find the sum of the first 25 terms of the series...11+14+17+20+...

first you find tn which is t25 and use the arithmetic formula which is t1+(n-1)d so it will be 11+(24)(3)=83.

Then you plug in the arithmetic series formula: Sn=25(11+83)/2=1175 and that is your answer.

The only thing i have problems with is what do i do with n when they dont tell me how many terms there are?